Two-dimensional solitons in conservative and parity-time-symmetric triple-core waveguides with cubic-quintic nonlinearity

TL;DR

This paper investigates two-dimensional solitons in triple-core waveguides with cubic-quintic nonlinearity, analyzing both conservative and parity-time-symmetric models, and identifies stable soliton solutions through stability analysis and simulations.

Contribution

It introduces and analyzes families of stable solitons in both conservative and $ ext{PT}$-symmetric triple-core waveguides with cubic-quintic nonlinearity, including stability and interaction studies.

Findings

Stable solitons exist in both models.

Linear stability analysis confirms soliton stability.

Numerical simulations support analytical results.

Abstract

We analyze a system of three two-dimensional nonlinear Schr\"odinger equations coupled by linear terms and with the cubic-quintic (focusing-defocusing) nonlinearity. We consider two versions of the model: conservative and parity-time ($\mathcal{PT}$) symmetric. These models describe triple-core nonlinear optical waveguides, with balanced gain and losses in the $\mathcal{PT}$-symmetric case. We obtain families of soliton solutions and discuss their stability. The latter study is performed using a linear stability analysis and checked with direct numerical simulations of the evolutional system of equations. Stable solitons are found in the conservative and $\mathcal{PT}$-symmetric cases. Interactions and collisions between the conservative and $\mathcal{PT}$-symmetric solitons are briefly investigated, as well.